Demand for digital subscriber line (DSL) service across existing twisted pair copper wires between a central office and a remote location is increasing. Typically, DSL services operate in accordance with DSL standards recommended by the Telecommunication Standardization Sector of the International Telecommunication Union (ITU). A family of DSL Recommendations from the ITU includes: G.992.1, G.992.2, G.991.1, G.996.1, G.994.1, G.997.1 and G.995.1. Recommendation G.995.1 provides an overview of these standards. Recommendations G.991.1, G.992.1, G.992.2 have developed techniques for transmitting a range of bit rates over the copper wires of the local network including high bit rates at relatively short distances, and lower bit rates at longer distances. In particular, the G.992.1 and G.992.2 recommendations are based on asymmetric digital subscriber line technology that has different data rates in each direction of transmission. The G.992.1 recommendation is referred to as G.dmt and uses a splitter to filter the voicegrade signals at the remote location. The G.992.2 recommendation is referred to as G.lite and does not use a splitter. Recommendations G.994.1, G.996.1 and G.997.1 support the G.992.1 and G.992.2 recommendations by providing common handshake, management and testing procedures. These standards allow substantial flexibility in implementation.
DSL services typically use a discrete multi-tone (DMT) signal to transmit data. A DMT signal has multiple sub-channels, each of which is assigned a frequency, also referred to as a carrier frequency or a tone, belonging to a discrete frequency band. Because individual sub-channels operate at different frequencies, the sub-channels may have different operating characteristics. For instance, more power may be used at higher frequencies. In addition, different numbers of bits may be loaded on different sub-channels in accordance with their capacity, which depends on frequency, power, signal-to-noise ratio and transmission line characteristics. Sub-channels that do not meet or exceed a minimum signal-to-noise ratio are not used. When initiating a DSL communication session, in the DSL modem, an initialization procedure at the receiver determines a number of bits to be grouped into a symbol for each sub-channel, that is, a number of bits per sub-channel, and exchanges that information with the transmitting DSL modem.
Quadrature amplitude modulation (QAM) is a technique to encode multiple bits into a QAM symbol. Each QAM symbol represents a distinct combination of bit values using a distinct combination of amplitude and phase of the carrier waveform. Each QAM symbol is represented by a QAM waveform.
Referring to FIG. 1, a signal space diagram depicts a constellation 14 of a group of distinct QAM symbols 18 that represents combinations of a group of bits. FIG. 1 depicts a 16-point G.992.2 constellation in which the number of bits b is equal to 4. In QAM, the amplitudes of two quadrature carriers are modulated and the carriers are combined. The x-axis 15 represents the amplitude of a first carrier, and the y-axis 16 represents the amplitude of a second carrier that is shifted in phase by 90° with respect to the first carrier. For example, the first carrier is a sine wave, while the second carrier is a cosine wave. Each point 19 represents a distinct combination of the modulated carriers and thus a distinct QAM symbol.
A constellation encoder encodes groups of bits into QAM symbols. For example, for QAM symbols that represent four bits, the constellation will have sixteen distinct QAM symbols and map each of the sixteen possible combinations of the four bits to a distinct one of the QAM symbols.
In DMT systems, the digital information is transformed by a modem into an analog form that is essentially a sequence of DMT symbol waveforms. Each DMT symbol bears information in an array of zeroes and ones, which has several bi-sized sub-arrays. Each sub-array corresponds to a QAM waveform representing a 2bi-point constellation. In other words, bi represents a number of bits per sub-channel i. A DMT symbol waveform is the superposition of these QAM waveforms. The channel itself is characterized by a signal-to-noise ratio γi, where γi represents the signal-to-noise ratio (SNR) at the ith carrier frequency.
In DMT systems, each sub-channel has a constellation encoder. Typically, in DMT systems, equal error protection is applied, and the number of bits per sub-channel bi is determined as follows: for each sub-channel, the bit error rate should not exceed a target bit error rate prior to decoding and retransmission pb. One conventional QAM error determination procedure as described by John G. Proakis, in Digital Communications, (Proakis) 1995, on p. 280 yields the QAM symbol error rate rather than the target bit error rate. Evaluating the equivalent bit error rate is known to be a complicated problem (See Proakis, p. 441). Therefore, it is typically assumed that the QAM symbol error rate is approximately equal to the bit error rate. However, this assumption is not precise and, for large QAM constellations, may misevaluate the bit error rate by a factor of ˜10.
The assumption of an equally probable constellation decoding error yields an average fraction of erroneous bits that approach ½ at large values of b. In other words, approximately half of the bits will be in error when a QAM symbol error occurs. This approach was earlier used in Proakis, p. 262 for 2b-ary orthogonal signals. However, this approach is not precise either. Because this assumption is used when determining the number of bits bi per sub-channel, an improved method and apparatus are needed to select the number of bits per sub-channel. Furthermore, this assumption does not accommodate for fluctuations in the bit error rate. The method and apparatus should also accommodate for fluctuations in the bit error rate.
Reed-Solomon encoding is a method of forward error correction used in DSL communications to detect and correct transmission errors, effectively increasing the signal-to-noise ratio of the communications channel. By encoding information, errors may be reduced without decreasing the data rate. In Reed-Solomon encoding, redundant symbols are added to information symbols to allow errors to be detected and corrected. As the number of redundant symbols increases, a greater level of noise may be tolerated. Among the transmission parameters to be selected in DSL communications are forward error correction (FEC) parameters for Reed-Solomon encoding. The FEC parameters determine the amount of information data in an information field, and a number of redundancy symbols that are associated with the information field of an information frame. Reed-Solomon encoding parameters for forward error correction are selected while executing the initialization procedure. During initialization, the channel is analyzed and FEC parameters are determined and exchanged. The ITU recommendations set a bit error rate (BER) standard of 10−7. The Reed-Solomon encoding parameters for forward error correction are selected based on, at least in part, the bit error rate standard and an average number of erroneous bits per QAM symbol. However, there is a need for selecting FEC parameters based on a more precise determination of the average number of erroneous bits per QAM symbol. In addition, there is a need to select FEC parameters based on a target bit error rate that accommodates for fluctuations in the average number of erroneous bits per QAM symbol.